# American Institute of Mathematical Sciences

December  2005, 4(4): 889-899. doi: 10.3934/cpaa.2005.4.889

## On a nonlinear parabolic system-modeling chemical reactions in rivers

 1 Department of Mathematics, Southwest Missouri State University, Springfield, MO 65804, United States 2 Department of Applied Mathematics, University of Colorado at Boulder 3 Department of Mathematics, University of Montana-Western, 710 S. Atlantic Street Dillon, MT 59725-3598, United States

Received  November 2004 Revised  May 2005 Published  September 2005

We study the global existence and qualitative properties of the solutions of nonlinear parabolic systems. Such systems commonly arise in situations pertaining to reactive transport. Particular examples include the modeling of chemical reactions in rivers or in blood streams.
In this paper, we first establish a maximum principle that generates a-priori bounds for solutions to a broad class of parabolic systems. Afterward, we develop an alternative technique for establishing global bounds on solutions to a specific system of three equations that belong to a different class of parabolic systems. Finally, we prove that the only bounded traveling wave solutions to this system are constants.
Citation: Wenxiong Chen, Congming Li, Eric S. Wright. On a nonlinear parabolic system-modeling chemical reactions in rivers. Communications on Pure & Applied Analysis, 2005, 4 (4) : 889-899. doi: 10.3934/cpaa.2005.4.889
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